How would I start writing criticism on a writer?i want to write a piece of literature which should be a criticism on some specific writing.

As others have noted, the first thing you need to do is determine your focus. What type of criticism are you writing. For instance, if you are focusing on a specific writer, you might begin by deciding which writer you wish to focus on. The, you can proceed in several ways, but two easy options are to choose a theme that is prevalent in several works by that author or tie that author's place in history or his or her personal life to elements of the works in question. Essentially, what you are looking for is patterns. You will find that most writers develop themes that reappear in all or most of their works, which makes it easier to identify them if you have read several works by the author in question.

On the other hand, if you are focusing on a specific work, then the first thing you need to do once you have decided what work you will be writing about is to look for themes, images, motifs, something in the plot or characterization that interests you and that you can make some sort of claim about (this will be your thesis).

As to research, a look at what other literary critics have said about the author or the work is a good way to generate ideas as well as to find proof from other sources that helps to support your ideas. Just remember that anything that you gather from research must be appropriately cited!